000131310 001__ 131310 000131310 005__ 20240319080957.0 000131310 0247_ $$2doi$$a10.1016/j.jtbi.2021.110942 000131310 0248_ $$2sideral$$a128084 000131310 037__ $$aART-2022-128084 000131310 041__ $$aeng 000131310 100__ $$aAlcalde Cuesta, F. 000131310 245__ $$aBernoulli and binomial proliferation on evolutionary graphs 000131310 260__ $$c2022 000131310 5203_ $$aIn this paper we introduce random proliferation models on graphs. We consider two types of particles: type-1/mutant/invader/red particles proliferates on a population of type-2/wild-type/resident/blue particles. Unlike the well-known Moran model on graphs –as introduced in Lieberman et al. (2005)–, type-1 particles can occupy in a single iteration several neighbouring sites previously occupied by type-2 particles. Two variants are considered, depending on the random distribution involving the proliferation mechanism: Bernoulli and binomial proliferation. By comparison with fixation probability of type-1 particles in the Moran process, critical parameters are introduced. Properties of proliferation are studied and some particular cases are analytically solved. Finally, by updating the parameters that drive the processes through a density-dependent mechanism, it is possible to capture additional relevant features as fluctuating waves of type-1 particles over long periods of time. In fact, the models can be adapted to tackle more general, complex and realistic situations. © 2021 Elsevier Ltd 000131310 536__ $$9info:eu-repo/grantAgreement/ES/DGA/E22-17R 000131310 540__ $$9info:eu-repo/semantics/openAccess$$aAll rights reserved$$uhttp://www.europeana.eu/rights/rr-f/ 000131310 590__ $$a2.0$$b2022 000131310 591__ $$aMATHEMATICAL & COMPUTATIONAL BIOLOGY$$b34 / 55 = 0.618$$c2022$$dQ3$$eT2 000131310 591__ $$aBIOLOGY$$b54 / 92 = 0.587$$c2022$$dQ3$$eT2 000131310 592__ $$a0.566$$b2022 000131310 593__ $$aAgricultural and Biological Sciences (miscellaneous)$$c2022$$dQ1 000131310 593__ $$aBiochemistry, Genetics and Molecular Biology (miscellaneous)$$c2022$$dQ2 000131310 593__ $$aStatistics and Probability$$c2022$$dQ2 000131310 593__ $$aMedicine (miscellaneous)$$c2022$$dQ2 000131310 593__ $$aModeling and Simulation$$c2022$$dQ2 000131310 593__ $$aApplied Mathematics$$c2022$$dQ2 000131310 593__ $$aImmunology and Microbiology (miscellaneous)$$c2022$$dQ2 000131310 594__ $$a4.9$$b2022 000131310 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/acceptedVersion 000131310 700__ $$aGuerberoff, G. 000131310 700__ $$0(orcid)0000-0002-1184-5901$$aLozano Rojo, Á.$$uUniversidad de Zaragoza 000131310 7102_ $$12006$$2440$$aUniversidad de Zaragoza$$bDpto. Matemáticas$$cÁrea Geometría y Topología 000131310 773__ $$g534 (2022), 110942 [19 pp.]$$pJ. theor. biol.$$tJournal of theoretical biology$$x0022-5193 000131310 8564_ $$s8784109$$uhttps://zaguan.unizar.es/record/131310/files/texto_completo.pdf$$yPostprint 000131310 8564_ $$s2943713$$uhttps://zaguan.unizar.es/record/131310/files/texto_completo.jpg?subformat=icon$$xicon$$yPostprint 000131310 909CO $$ooai:zaguan.unizar.es:131310$$particulos$$pdriver 000131310 951__ $$a2024-03-18-13:46:27 000131310 980__ $$aARTICLE